Research Article Modelling of a PMSG Wind Turbine with ...

Research ArticleModelling of a PMSG Wind Turbine with Autonomous Control

Chia-Nan Wang, Wen-Chang Lin, and Xuan-Khoa Le

Industrial Engineering and Management Department, National Kaohsiung University of Applied Sciences,415 Chien Kung Road, Sanmin District, Kaohsiung 80778, Taiwan

Correspondence should be addressed to Chia-Nan Wang; [email protected]

Received 26 February 2014; Accepted 7 April 2014; Published 27 May 2014

Academic Editor: Her-Terng Yau

Copyright © 2014 Chia-Nan Wang et al.This is an open access article distributed under theCreativeCommonsAttribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The aim of this research is to model an autonomous control wind turbine driven permanent magnetic synchronous generator(PMSG) which feeds alternating current (AC) power to the utility grid. Furthermore, this research also demonstrates the effectsand the efficiency of PMSGwind turbine which is integrated by autonomous controllers. In order for well autonomous control, twovoltage source inverters are used to control wind turbine connecting with the grid.The generator-side inverter is used to adjust thesynchronous generator as well as separating the generator from the grid when necessary. The grid-side inverter controls the powerflowbetween the direct current (DC) bus and theAC side. Both of them are oriented control by space vector pulsewidthmodulation(PWM)with back-to-back frequency inverter.Moreover, the proportional-integral (PI) controller is enhanced to control both of theinverters and the pitch angle of the wind turbine. Maximum power point tracking (MPPT) is integrated in generator-side inverterto track the maximum power, when wind speed changes.The simulation results in Matlab Simulink 2012b showing the model havegood dynamic and static performance. The maximum power can be tracked and the generator wind turbine can be operated withhigh efficiency.

1. Introduction

Renewable energy such as wind power is an importantsolution to reducing carbon emissions. Nowadays, with therapid development of wind power technology, wind powercan be converted into a useful form of energy, such asusing wind turbines—the device that converts kinetic energyfrom the wind—to make electrical power. In fact, sincewind power, as an alternative to fossil fuels, produces nogreenhouse gas emissions during operation, it makes ahuge difference to our environmental impact. Despite verysignificant advancements and influence to the environment,wind power costs continue to be greater than the existinglow-carbon alternative such as natural gas. Therefore, muchresearch remains to be done in order to improve wind tur-bines’ behaviour and to make them cost-efficient to competewith the traditional energy such as natural gas.

There are many kinds of variable speed generators usedfor wind turbine. According to the reference [1, 2], althoughdoubly fed induction generator (DFIG) is more broadly usedthan permanent magnetic synchronous generator (PMSG)today, PMSG has some advantages which are counted as

experts. Particularly, PMSG is direct drive, has slow rotationspeed, does not have rotor current, and can be used withoutgearbox.The high efficiency and lowmaintenance will reducethe cost that is the most concern to invest. However, PMSGstill has some drawbacks. It needs electromagnetic field withthe flexible structure, which leads to the high standard of theproduction as well as of the operation. Furthermore, variablespeed of the generator has to be known by power inverter too.

According to the continuous development of wind powertechnology, the efficiency of inverter device, facing sometough issues, plays an important role in the improvement ofwind power generation system performance.They need to beenhanced by novel controller [3] to improve the efficiencyand the reliability. Inside them, MPPT integrating with theback to back space vector PWM [4] is the advantage controlnovel in [5–8], which is used to measure the rotor speedand compare with the calculated optimal rotor speed. Onthe other hand, not only does the inverter take an advantagein efficiency control but also the pitch angle controller takesanother important part of wind turbine. It is integrated toadjust the aerodynamic torque of the wind turbine when thisstudy rates wind speed.

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 856173, 9 pageshttp://dx.doi.org/10.1155/2014/856173

2 Mathematical Problems in Engineering

System management

ACDC

DCAC

PMSG

Transformer

GridFilter

Control

Rotor speedPitch

Wind speed

InverterRectifier

Multipole generator

(a)

Grid

Grid-side inverter

Generator-side inverter

PMSG

Transformer

Udc

(b)

Figure 1: General wind turbine PMSG system with control schemes (a) and (b).

This study will model the whole wind turbine systemincluding physical part of permanent magnet synchronousgenerator and control strategies for generator side and gridside as well as the pitch angle controller to depict the effectsand the efficiency of PMSG by autonomous controllers. Themodel system and control strategies contain a PMSG windturbine model, a pitch angle control model, generator-sideinverter control model, and grid-side inverter control model.The generator-side inverter and grid-side inverter controlleradopt the back to back space vector PWM to enhance theperformance of MPPT as well as decoupling control of theactive and reactive power by adjusting the current of 𝑑-axisand 𝑞-axis of their side inverters. Furthermore, conventionalPI controller is also used to improve the control strategy.It is integrated in generator-side inverter, grid-side inverter,and the pitch angle controller. Matlab Simulink 2012b asreference [9] is conducted to simulate and demonstrate theperformance. The results will demonstrate the effects andthe efficiency of PMSG wind turbine which is integrated byautonomous controllers.

2. Model of PMSG Wind Turbine

2.1. Structure of PMSG Wind Turbine. The basic of PMSGwind turbine structure shown on Figure 1 is defined as [10].The wind turbine generates torque from wind power. Thetorque is transferred through the generator shaft to the rotorof the generator. The generator produces an electrical torque,and the difference between the mechanical torque from thewind turbine and the electrical torque from the genera-tor determines whether the mechanical system accelerates,decelerates, or remains at constant speed.

The generator is connected to a three-phase inverterwhich rectifies the current from the generator to charge aDC-link 𝑈𝑑𝑐 capacitor [11]. The DC-link 𝑈𝑑𝑐 feeds a secondthree-phase inverter which is connected to the grid througha transformer. Through the control system, the informationof wind speed, pitch angel, rotor RPM, and inverter outputis accepted to compare with the grid-side data. Therefore,this information is solved by using a digital signal processing

system to produce the correct signal to control these compo-nents.Themain goal is to synchronize with utility grid and toexport power to it.

2.2. Model of Wind Turbine. Thewind turbine is used for theconversion of wind kinetic energy to mechanical work. Onthe basis of relationships for the calculation, it is possible toexpress the value 𝑃𝑚 of the aerodynamic wind turbine power[1, 12, 13]:

𝑃𝑚 = 0.5 ⋅ 𝜌 ⋅ 𝐴 ⋅ V3 ⋅ 𝐶𝑝 (𝜆, 𝛽) . (1)

Here, 𝜌 is the air density, 𝐴 = 𝜋 ⋅ 𝑅2 is the blades swept

of the turbine, V is wind speed, and 𝐶𝑝(𝜆, 𝛽) is the powercoefficient, which expresses the relationship between the tipspeed ratio 𝜆 and the pitch angle 𝛽.

The power coefficient 𝐶𝑝(𝜆, 𝛽) is as

𝐶𝑝 (𝜆, 𝛽) = 0.22 (116

𝛾− 0.4 ⋅ 𝛽 − 5) ⋅ exp(−

12.5

𝛾) , (2)

with1

𝛾=

1

𝜆 + 0.089−

0.035

𝛽3 + 1. (3)

The relationship between the wind speed and the rotorspeed is defined as tip speed ration 𝜆:

𝜆 =𝑅 ⋅ 𝜔

V, (4)

where 𝜔 is the blades angular velocity and 𝑅 is the rotorradius.

From the value of the rotational motion performance, itis possible to determine the value of the torque 𝑇𝑚 acting onthe shaft as follow:

𝑇𝑚 =𝑃𝑚

𝜔. (5)

These formulas are evident that the instantaneous valuesof the performance, respectively, of the mechanical torque,

Mathematical Problems in Engineering 3

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2.5 5 7.5 10 12.5 15

Cp

(Cp max , 𝜆opt )

−0.1

𝜆

𝛽 = 0∘

𝛽 = 5∘

𝛽 = 10∘

𝛽 = 15∘

𝛽 = 20∘

𝛽 = 30∘

Figure 2: The curve of power wind turbine coefficient.

0 5 10 15 20 25 30 35 40 45 50 55

2.5

0

5

7.5

10

12.5

15

17.5

20

Optimalline

MPP

11m/s

9m/s

7m/s5m/s

𝜔 (rad/s)

� =

� =

� =

� =

Pow

erPm

(kW

)

Figure 3:The curve to illustrate the relationship between power andwind speed.

are dependent on the wind speed very much. On the basisof these equations, it is possible to build the model, whichstructure is shown in Figure 4, of the wind turbine inSimulink platform.

Figure 2 shows the curve of power wind turbine coeffi-cient. It reveals that 𝐶𝑝 achieves the maximum value at theparticular 𝜆opt.

Figure 3 shows that the rotational speed is a function,in which the power captured in turbine blade obtains themaximum output at the particular rotational speed, while thepitch angle is constant. Hence, 𝜆 should be kept at 𝜆opt tomaximize the wind energy.

In Figure 4, 𝑓(𝑢) of Lambda, Gama, and 𝐶𝑝 are definedin the order of equations (4), (3), and (2). If wind speed is inthe range from 3m/s to cut out 25m/s, it is combined to formturbine torque 𝑓(𝑢) as (1) and (5).

2.3. Model of Permanent Magnet Synchronous Generator. Thegeneratormodel is implemented entirely in𝑑𝑞-coordinates. Itmeans that there are noAC-states in themodel.The generatoris modelled with DC voltages and currents in a rotor-fixedrotating coordinate system which is illustrated in Figure 5.

The equations for the 𝑑-axis and 𝑞-axis currents are definedin [1–3] as

𝑑𝑖𝑠𝑑

𝑑𝑡= −

𝑅𝑠𝑎

𝐿 𝑠𝑑

𝑖𝑠𝑑 + 𝜔𝑠

𝐿 𝑠𝑞

𝐿 𝑠𝑑

𝑖𝑠𝑞 +1

𝐿 𝑠𝑑

𝑢𝑠𝑑

𝑑𝑖𝑠𝑞

𝑑𝑡= −

𝑅𝑠𝑎

𝐿 𝑠𝑞

𝑖𝑠𝑞 − 𝜔𝑠 (𝐿 𝑠𝑑

𝐿 𝑠𝑞

𝑖𝑠𝑑 +1

𝐿 𝑠𝑞

𝜓𝑝) +1

𝐿 𝑠𝑞

𝑢𝑠𝑞.

(6)

The equation of the electromagnetic torque in the rotor is

𝑇𝑒 = 1.5𝑃

2[𝜓𝑝𝑖𝑠𝑞 + 𝑖𝑠𝑑𝑖𝑠𝑞 (𝐿 𝑠𝑑 − 𝐿 𝑠𝑞)] . (7)

There, 𝑖𝑠𝑑, 𝑖𝑠𝑞, 𝑢𝑠𝑑, and 𝑢𝑠𝑞 are the 𝑑-axis and 𝑞-axiscurrents and voltages respective stator resistance; 𝜔𝑠 is thebasic electrical angular frequency of the generator; 𝐿 𝑠𝑑 and𝐿 𝑠𝑞 are the inductance of generator;𝜓𝑝 is permanent flux; 𝑅𝑠𝑎is the resistance of stator; and 𝑃 is the number of poles.

Figure 5 shows the 𝑑𝑞-coordinates frame of the PMSGwith 𝜃 being the angle between 𝑑-axis and the main statoraxis.

3. Autonomous Control ofPMSG Wind Turbine

3.1. Generator-Side Inverter Controller. The generator-sideinverter is controlled to catchmaximumpower fromavailablewind power. According to (7), in order to control theelectromagnetic torque 𝑇𝑒, this study just controls the 𝑞-axiscurrent 𝑖𝑠𝑞 with the assumption that the 𝑑-axis current 𝑖𝑠𝑑 isequal to zero. Furthermore, [3, 14] show that, in order to catchmaximum power, the optimum value of the rotation speed isadjusted. The tip speed ratio 𝜆 is taken into account due tothe equation being addressed as follow:

𝜔ref =𝜆opt ⋅ V

𝑅. (8)

There,𝜔ref is the blades angular velocity reference and𝜆optis the tip speed ratio optimum.

From (6), it is calculated that

𝑈𝑠𝑑 = 𝑅𝑠𝑎 ⋅ 𝑖𝑠𝑑 − 𝜔𝑠 ⋅ 𝐿 𝑠𝑞 ⋅ 𝑖𝑠𝑞 +𝑑𝑖𝑠𝑑

𝑑𝑡⋅ 𝐿 𝑠𝑑

𝑈𝑠𝑞 = 𝑅𝑠𝑎 ⋅ 𝑖𝑠𝑞 + 𝜔𝑠 ⋅ 𝐿 𝑠𝑑 ⋅ 𝑖𝑠𝑑 +𝑑𝑖𝑠𝑞

𝑑𝑡⋅ 𝐿 𝑠𝑞 + 𝐸𝑠,

(9)

with 𝐸𝑠 = 𝜔𝑠 ⋅ 𝜓𝑝 being the permanent flux linkages.The generator-side inverter control schematic is illus-

trated in Figure 6. Through the MPPT in [5], the errorof 𝜔ref is produced. Therefore, the error of 𝜔ref and 𝜔𝑠 isrescued to PI controller to produce 𝑞-axis current component𝑖𝑠𝑞 ref which put into space vector pulse width modulation(SVPWM).The 𝑑-axis current 𝑖𝑠𝑑 ref is set to zero because the𝑑-axis current control is adopted. Consequently, through theSVPWM containing voltage feed-forward compensation, thepower factors of the generator are calculated and controlledwell.


1

3

Wind speedmaximum

Wind speedminimum

25

Turbinetorque

Relationaloperator 2

Relationaloperator

Logicaloperator

AND

LambdaGama

Wind speed3

Pitch angle2

1

≤

≥

Cp

f(u)

f(u)

f(u)

f(u)

Tm

Rotor seed Wm

Figure 4: Model of the aerodynamic of wind turbine in Matlab Simulink 2010b.

sA

sB sC

N

S

𝛼-axisd-axis

𝛽-axis

q-axis

𝜃

𝜔s

Figure 5: The 𝑑𝑞-coordinate frame of the PMSG.

3.2. Grid-Side Inverter Controller. The goal of the grid-sideinverter is keeping the stability of the DC-line voltage [15–18] as well as controlling the active and reactive power [3, 19].For the grid/transformer inductance, the model is given asfollows:

𝑢𝑑 = 𝑒𝑑 − 𝑅 ⋅ 𝑖𝑑 + 𝜔 ⋅ 𝐿 ⋅ 𝑖𝑞 − 𝐿 ⋅𝑑𝑖𝑑

𝑑𝑡,

𝑢𝑞 = −𝑅 ⋅ 𝑖𝑞 − 𝜔 ⋅ 𝐿 ⋅ 𝑖𝑑 − 𝐿 ⋅𝑑𝑖𝑞

𝑑𝑡.

(10)

Here, 𝑒𝑑 is the 𝑑-axis output voltage of the grid, respec-tively,𝜔 is the angular frequency in electrical degree of grid,𝑅is the resistance,𝐿 is the inductance, respectively, and 𝑖𝑑 and 𝑖𝑞are the currents of𝑑-axis and 𝑞-axis. By (10), it is easy to figureout that the current of 𝑑-axis and 𝑞-axis can be controlled tomoderate the active and reactive power. In Figure 7, the loopvoltage and the loop current are illustrated.The inner currentloop is controlled through PI controller similar to generator-side inverter controller. The output voltage loop produces PIcontroller for calculating the error between 𝑈𝑑𝑐 and 𝑈𝑑𝑐 refto produce 𝑖𝑑 ref. Therefore, 𝑞-axis current is set to be zero to

decoupling control of the active power 𝑃 and reactive power𝑄 by moderating the 𝑑-axis current 𝑖𝑑 and the 𝑞-axis current𝑖𝑞.

3.3. Pitch Angle Controller. The system of aerodynamic con-trol plays an important role in regulating the mechanicalpower. Pitch angle controller is based on the principle whichis changing the blades angle at the revolutions over themaximal generator speed as well as protecting the generatorbefore overloading at high wind speeds. The optimal anglefor the wind speed below the nominal value is approximatelyzero and then it increases with the wind speed growing. Ithas considerable impact on the performance coefficient andon the value of the turbine torque in [20].

In this controller, illustrated in Figure 8, the speed of thegenerator which is the input is compared with its referencevalue through PI controller to have the output value of thepitch angle of the blades, which changes the performancecoefficient of the turbine.

3.4. Maximum Power Point Tracking (MPPT). In thegenerator-side inverter, MPPT produces the 𝜔ref for thecomparative PI controller. According to Figure 3 and [5–8],the wind turbine coefficient achieves the maximum for thetip speed, when the pitch angle 𝛽 = 0. In terms of everywind speed, there exists a specific point to get the maximumoutput. Hence, in order to control the maximum power inevery wind speed, the MPPT tracks the continuous line andoptimal line in Figure 9.

The tip speed ratio is kept at constant value for allmaximum power points, while the relationship between thewind speed and thewind turbine generator speed is explainedas follows:

Ω𝑛 = 𝜆𝑛

𝑉𝑛

𝑅, (11)

withΩ𝑛 being the optimal rotation wind turbine generator atthe wind speed 𝑉𝑛.

The MPPT control strategy is based on monitoring thewind turbine generator output power using measurements ofthe wind turbine generator output voltage and current as well


Generator-sideinverterPMSG

abcdq

d/dt

SVPWM

dq

PIMPPT

PI PI

−+

−

+

++

+

+

−

−

+

ia ib ic

𝜃

isq isd

𝜔s

𝜔ref 𝜔s · Lsq

𝜔s · Lsd

isq

isd

isq ref

isd ref

𝛼𝛽

Es

Figure 6: Scheme of generator-side inverter controller.

Grid-sideinverter

SVPWM

dq

PI PI

+

+

+

PI

abcdq

+ +

−

−

+ −

+ −

abc

Grid

ia ib ic

𝜃𝛼𝛽

𝛼𝛽

id iq

ud

ua ub uc

id

iq

Udc

Udc ref

iq ref = 0

id ref

𝜔 · L

𝜔 · L

Figure 7: Scheme of grid-side inverter controller.

as directly modelling the dc/dc converter duty cycle, which isfollowed by the comparison of among output power values.

4. Simulation Analysis

In order to verify themodel of the whole autonomous controlsystem design, Matlab 2010b is used to simulate this systemdesign in Figure 10.

Model of wind turbine is in wind turbine; models of con-trol system of generator-side inverter and grid-side inverterare included in Subsystem 1 and Subsystem 2. The MPPTcontroller and PI controller are also included in Subsystem1 and Subsystem 2. The pitch angle controller is completelymodelled in wind turbine. In this simulation, the windturbine PMSGmodel obtains the wind speed and provides anoptimal reference speed to control the system.The simulationresults are shown in Figures 11–14.


Pitch angle1

Nominal speed-C-

DiscretePI controller

PIGenerator speed

1 +−

Figure 8: Model of pitch angle controller inMatlab Simulink 2010b.

Optimal line

Maximumpower point

W/G

pow

er (W

)

W/G Speed (rad/s)

VnV4

V3V2

V1

Ω2 . . . ΩnΩ1

Pn

P4

P3

P2

P1

Wind speed V1 < V2 < . . . Vn

Figure 9: Wind turbine generator power curve at various windspeeds.

The main system parameters are listed in Table 1 accord-ing to the design consideration. The original states of thesystem are zero. When wind speed is 12m/s, optimal speedof PMSG is obtained. Pitch angle controller catches theoptimum tip speed ratio at 8 and optimum power coefficientat 0.4 through the maximum power point tracking. On theother hand, grid-side inverter models the output voltagewith the DC-link voltage 1200V in accordance with DC-link capacitor 15000 𝜇F. After all, PMSG wind turbine withautonomous control system produces the grid line voltage at900V.

Figure 11 shows the waves of DC-link voltage, the voltageis produced by grid-side inverter andA-phase voltage feedingto the grid. Through the results, it is admitted that DC-voltage is well controlled in stabilizing performance with thefluctuation being about 25%. When 𝑉𝑎𝑏 passes through theinverter, load voltage slightly fluctuates by the late modellingduring 0 s to 0.08 s. After that, the load voltage can be kept instable output.

Figure 12 shows the wave forms of 𝑑-current, voltagephase of PMSG, and 𝑑-voltage reference. According to theresults, it can be revealed that, despite the usual changeof wind speed, the 𝑑-axis current is still modelled to bemaintained at zero level off.

The voltage phase per unit (pu) of PMSG is decreasedafter the beginning stage; however, it keeps constant value atthat later time.

Figure 13 shows the waves of three-phase voltage andcurrent of the grid when autonomous PMSG wind turbineis operated at stable state. Voltage phase almost opposes thecurrent phase.

Figure 14 performs the waves of active power and reactivepower decoupling control.When thewind turbine catches the

Table 1: The parameters of autonomous control PMSG windturbine.

PMSG

Rated voltage of stator: 5 KVRated frequency of stator: 50HzRated rotor torque: 450N⋅mStator phase resistance: 0.01ΩArmature inductance: 0.03H𝑑-axis inductance: 5.5mH𝑞-axis inductance: 3.75mHNumber of poles: 56

Wind turbine

Rated power: 2MWBlades radius: 35mOptimum tip-speed ratio: 8Optimum power coefficient: 0.4Air density: 1.225 kg/m3

Cut-in wind speed: 3m/sRated wind speed: 12m/sCut-out wind speed: 25m/s

Others

Grid line voltage: 900VDC-link voltage: 1200VDC-link capacitor: 15000 𝜇FTransformer output voltage: 12 KVFrequency: 50Hz

wind speed at rate 4m/s, PMSG begins to operate.Therefore,the pitch angle is controlled to catch themaximum coefficientat rate 13m/s wind speed. After 0.14 s, the generator-sideinverter and the grid-side inverter are cooperated to controlthe voltage through controllers. The wind turbine gets thestable output power to the grid with standard voltage,frequency, and phase.

By the autonomous control, including pitch angle con-troller, generator-side inverter, and grid-side inverter, thewind turbine is able to achieve the highest efficiency.Throughthe MPPT strategy as well as pitch angle controller, it cancatch the maximum wind energy and operate at optimalspeed ratio.

5. Conclusions

This study analyzes the control strategies as well as modelsand designs and simulates the whole autonomous system ofPMSG wind turbine feeding AC power to the utility gridin Matlab Simulink 2010b. The simulation results show thatthe combination of pitch angle controller, generator-sideinverter controller, and grid-side inverter controller has gooddynamic and static performance. The maximum power canbe tracked and the generator wind turbine can be operatedin high efficiency. DC-link voltage is kept at stable level fordecoupling control of active and reactive power. Hence, theoutput will get the optimum power supply for the grid.


PowerGUI

Discrete,

Wind turbine

Rotor speed Wm

Wind speedTm

Wind speed

V

v+−

v+−v+

−Universal bridge 2

g

A

B

C

+

−

Universal bridge 1

g

A

B

C

+

−

Transformer

A

B

C

a

b

cThree-phase source

A

B

C

Subsystem 1

Pulse

Subsystem 2

Pulse

Permanent magnetsynchronous machine

mA

B

C

Measure 2

A

B

C

a

b

c

Measure 1

A

B

C

a

b

c

Measure

A

B

C

a

b

c

LC filter 1

A

B

C

A

B

C

LC filter

A

B

C

A

B

C

Theta

A B C

VdcVdc

Vdc

Vab load

Vab load

Vdc

Vabc

Vabc

Vab inverVab inver

S

N

[Vabc ]

[Iabc ]

[Vdc]

[Vabc ]

[Iabc ] Iabc

Iabc

2e − 005 s.

⟨rotor angle thetam (rad)⟩

⟨rotor speed wm (rad/s)⟩

Yg Yg

Tm

Ts =

Figure 10: Simulation model of autonomous control PMSG wind turbine.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.180

500100015002000

Vdc

(a)

0500

1000

−1000−500

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Vab load

(b)

05

10

Time offset: 0

−5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

×105 Vab inverter

(c)

Figure 11: DC-link voltage, load voltage, and inverter voltage.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

00.5

1

−2

−1−1.5

−0.5

d current

(a)

0 Phase

−6−5−4−3−2−1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

(b)

0.10.20.30.4

Time offset: 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Vd reference

(c)

Figure 12: 𝑑-current, voltage phase of PMSG, and 𝑑-voltage reference (pu).


0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34

0200400600 Voltage

−600

−400

−200

(a)

0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34

01000200030004000

Current

Time offset: 0

−4000−3000−2000−1000

(b)

Figure 13: Three-phase voltage and current of the grid.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

024 Active power

−10−8−6−4−2

×105

(a)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

0 Reactive power

Time offset: 0

−2

−1

−2.5

−1.5

−0.5

×106

(b)

Figure 14: Active and reactive power.

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper.

References

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